Subdividing a geometric domain into polyhedral elements is desirable in numerous technical fields. For example, it is desirable to subdivide a geometric domain into polyhedral elements when performing a three-dimensional numerical simulation using polyhedral discretization. Robustness of conventional processes for performing domain decomposition (e.g., the subdivision of a geometric domain into polyhedral elements) is not trivial. Generally, domain decomposition breaks down a domain into a finite number of cells with certain desired properties, such as positive Jacobian, element convexity, and planar facets. A domain decomposition also defines how a point in the domain is assigned to a cell, and how each cell in the domain decomposition identifies cells in close proximity thereto.
Several different approaches have been proposed for performing domain decomposition over geometric domains. These approaches, however, are associated with numerous deficiencies. In particular, conventional Voronoi domain decomposition (VDD) approaches rely on clipping, where facets of one or more Voronoi cells extend beyond a boundary of the geometric domain, and such facets are clipped. This may result in a clipped Voronoi cell having undesirable properties, such as a relatively large aspect ratio. Additionally, clipping may result in creation of cells that are non-convex and/or not star-shaped. Thus, while Voronoi domain decomposition of a geometric domain may produce desirable properties for many applications, there is currently a lack of a robust approach for performing Voronoi domain decomposition that does not rely upon clipping.